Physics Fundamentals
2nd Edition
ISBN: 9780971313453
Author: Vincent P. Coletta
Publisher: PHYSICS CURRICULUM+INSTRUCT.INC.
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Chapter 4, Problem 34P
To determine
To Find: The value of
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(a) Show that the rate of change of the free-fall acceleration with vertical position near the Earth's surface is
dg
2GM
3--5
dr
RE³
This rate of change with position is called a gradient.
(b) Assuming his small in comparison to the radius of the Earth, show that the difference in free-fall acceleration between two points separated by vertical distance h is
|Agl
=
2GMEh
RE
3
(c) Evaluate this difference for h = 41.25 m, a typical height for a fifteen-story building. (Enter your answer in m/s².)
m/s²
(a) Show that the rate of change of the free-fall acceleration with vertical position near the Earth's surface is
dg
dr
2GM
RE³
This rate of change with position is called a gradient. (Submit a file with a maximum size of 1 MB.)
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(b) Assuming his small in comparison to the radius of the Earth, show that the difference in free-fall acceleration between two points separated by vertical distance h is
2GM Eh
|Ag❘ =
RE
(Submit a file with a maximum size of 1 MB.)
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(c) Evaluate this difference for h = 41.25 m, a typical height for a fifteen-story building. (Enter your answer in m/s².)
m/s²
68
Two small spaceships, each with mass m = 2000 kg, are
in the circular Earth orbit of Fig. 13-50, at an altitude h of 400 km.
Igor, the commander of one of the
ships, arrives at any fixed point in
the orbit 90 s ahead of Picard, the
commander of the other ship. What
are the (a) period T, and (b) speed
Vo of the ships? At point P in Fig.
13-50, Picard fires an instantaneous
R
M
burst in the forward direction, re-
ducing his ship's speed by 1.00%.
After this burst, he follows the el-
liptical orbit shown dashed in the
figure. What are the (c) kinetic en-
ergy and (d) potential energy of his ship immediately after the
burst? In Picard's new elliptical orbit, what are (e) the total energy
E, (f) the semimajor axis a, and (g) the orbital period T? (h) How
much earlier than Igor will Picard return to P?
Fig. 13-50 Problem 68.
Chapter 4 Solutions
Physics Fundamentals
Ch. 4 - Prob. 1QCh. 4 - Prob. 2QCh. 4 - Prob. 3QCh. 4 - Prob. 4QCh. 4 - Prob. 5QCh. 4 - Prob. 6QCh. 4 - Prob. 7QCh. 4 - Prob. 8QCh. 4 - Prob. 9QCh. 4 - Prob. 10Q
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- In an atom an electron moves about its nucleus in a circular path of radius 5.30 x 10-11 m, with a speed of 2.20 x 106 m/s. Find the acceleration of the electron and the centripetal force. (mass of electron = 9.11 x 10-31 kg)arrow_forward(c) A small object was found to drop above the surface of a big planet with no initial velocity and it fell 13.5 m in 3 s. If the radius of the planet is 5.82 x 10° m, calculate the small object's acceleration during the fall and the mass of the big planet.arrow_forwardIn Fig. 13-32, a square of edge length mị 20.0 cm is formed by four spheres of masses m; = 5.00 g, m, = 3.00 g, m3 = 1.00 g, and m4 = 5.00 g. In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m, = 2.50 g? •7 One dimension. In Fig. 13-33, two point particles are fixed on an x axis sepa- mg roted bu dictonged Porticle 4 hor morc m •6arrow_forward
- The radius of Earth is about 6400 km. How far upward from the surface would a body feel a value of gabout half of that on the surface of Earth?arrow_forward(c) As an aerospace engineer, your spaceship orbits the Moon at a height of 20 km. Assuming it is subject only to the gravitational pull of the Moon, find its speed and the time it takes for one orbit. For the Moon, its mass is 7.34 x 1022 kg and its radius is 1.738 x 10 m.arrow_forward*15-112. A toboggan and rider, having a total mass of 150 kg, enter horizontally tangent to a 90° circular curve with a velocity of va = 70 km/h. If the track is flat and banked at an angle of 60°, determine the speed vg and the angle e of “descent," measured from the horizontal in a vertical x-z plane, at which the toboggan exists at B. Neglect friction in the calculation. VA = 70 km/h 60° TA 60 m 60° r = 57 m 55 m 90° 55 marrow_forward
- A mass (3.5 kg ) is attached to a string (1.7 m) and swung vertically in a circle from the free end of the string. Find the tension in (newtons) in the string when the mass is at the highest point of the circle with a speed of 9 m/s?arrow_forwardAt what altitude h above the north pole is the weight of an object reduced to 27% of its earth-surface value? Assume a spherical earth of radius R and express h in terms of R. Answer: h= i R.arrow_forwardThe moon orbits the earth along a path of radius 3.84 x 108 m , a spaceship of mass 30000 Kg orbits the Earth along a path of radius 2.8 x 108 m. calculate: a) The gravitational force exerted on the spaceship when it is at the line joints the centers of the earth and the moon. b) the gravitational field strength of the Earth at a point that locates at the orbit of the spaceship. G = 6.67 x 10-11 Nm2/Kg2 ME = 6 x 1024 Kg , Mm = 7.35 x 1022 Kgarrow_forward
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